## Làm gấp bài 4 cho mk nhé

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Làm gấp bài 4 cho mk nhé

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8 tháng 2020-10-29T17:42:49+00:00 1 Answers 55 views 0

$\begin{array}{l} \dfrac{a}{{2009}} = \dfrac{b}{{2010}} = \dfrac{c}{{2011}}\\ = \dfrac{{a – b}}{{2009 – 2010}} = \dfrac{{a – b}}{{ – 1}} = – \left( {a – b} \right)\\ = \dfrac{{b – c}}{{2010 – 2011}} = – \left( {b – c} \right)\\ = \dfrac{{c – a}}{{2011 – 2009}} = \dfrac{1}{2}\left( {c – a} \right)\\ \Rightarrow \dfrac{a}{{2009}} = – \left( {a – b} \right) = – \left( {b – c} \right) = \dfrac{1}{2}\left( {c – a} \right)\\ \Rightarrow \left\{ \begin{array}{l} a – b = – \dfrac{a}{{2009}}\\ b – c = – \dfrac{a}{{2009}}\\ c – a = 2.\dfrac{a}{{2009}} \end{array} \right.\\ \Rightarrow M = 4.\left( {a – b} \right)\left( {b – c} \right) – {\left( {c – a} \right)^2}\\ = 4.\left( { – \dfrac{a}{{2009}}} \right).\left( { – \dfrac{a}{{2009}}} \right) – {\left( {2.\dfrac{a}{{2009}}} \right)^2}\\ = 4.{\left( {\dfrac{a}{{2009}}} \right)^2} – 4.{\left( {\dfrac{a}{{2009}}} \right)^2}\\ = 0 \end{array}$